I would agree to add a Edit > Select all at all levels menu item, but I fear that introducing an other Select at all levels select tool might be too misleading for many users, even if your use case is interesting.

I hadn't considered that -- you're right, I think most people would be confused by a separate tool/menu option like that.

Another option that might be less confusing could be to make a tool labeled something like "move entire design" that when chosen would automatically select everything on the plan at all levels, and then allow to to click and drag it all to another spot.

Combined with Copy > Cut / Paste or with selection toggling using the shift key, the Select all at all levels menu item could still be helpful for you, right?

Sure, that would work just as well.